Binary Subtraction Section 3-9 Mano & Kime. Binary Subtraction Review from CSE 171 Two’s Complement Negative Numbers Binary Adder-Subtractors 4-bit Adder/Subtractor.

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Presentation transcript:

Binary Subtraction Section 3-9 Mano & Kime

Binary Subtraction Review from CSE 171 Two’s Complement Negative Numbers Binary Adder-Subtractors 4-bit Adder/Subtractor in VHDL

Half Subtractor CABD A 0 B 0 D 0 C 1

Full Subtractor C i A i B i D i C i CiCi AiBiAiBi DiDi D i = C i $ (A i $ B i ) Same as S i in full adder

Full Subtractor C i A i B i D i C i+1 CiCi AiBiAiBi C i+1 C i+1 = !A i & B i # C i !A i & !B i # C i & A i & B i

Full Subtractor C i+1 = !A i & B i # C i !A i & !B i # C i & A i & B i C i+1 = !A i & B i # C i & (!A i & !B i # A i & B i ) C i+1 = !A i & B i # C i & !(A i $ B i ) Recall: S i = C i $ (A i $ B i ) C i+1 = !A i & B i # C i & !(A i $ B i )

Full Subtractor S i = C i $ (A i $ B i ) C i+1 = !A i & B i # C i & !(A i $ B i ) half subtractor

Binary Subtraction Review from CSE 171 Two’s Complement Negative Numbers Binary Adder-Subtractors 4-bit Adder/Subtractor in VHDL

Negative Numbers Subtract by adding ’s complement Ignore carry

Negative Numbers 10’s complement : Subtract from Take 9’s complement and add

Negative Numbers 2’s complement: Subtract from Take 1’s complement and add

Finding 2’s Complement Copy all bits to first 1 2’s complement 0001 Complement remaining bits 0101

Negative Number Take 2’s Complement = 4B 16 = = B5 16 = FF -4B B4 +1 B5

Negative Number Take 2’s Complement 1 10 = = = FF 16 = = = = =

Signed Numbers 4-bit: 8H = -8 to 7H = to bit: 80H = -128 to 7F = bit: 8000H = -32,768 to 7FFFH = +32, bit: H = -2,147,483,648 to 7FFFFFFFH = +2,147,483,647

Binary Subtraction Review from CSE 171 Two’s Complement Negative Numbers Binary Adder-Subtractors 4-bit Adder/Subtractor in VHDL

Block Diagram of Binary Adder-Subtractor

Adder/Subtractor A 0 B 0 D 0 C 1 A 0 B 0 S 0 C 1 Half adder Half subtractor E = 0: Half adder E = 1: Half subtractor

Adder/Subtractor-1 i+1 E = 0: Full adder E = 1: Full subtractor

C i A i B i S i C i C i A i B i S i C i+1 Full Adder Reordered Full Adder C i A i B i D i C i+1 Full Subtractor NOT

Making a full adder from a full subtractor

Adder/Subtractor-2 E = 0: 4-bit adder E = 1: 4-bit subtractor

4-bit Subtractor: E = 1 +1 Add A to !B (one’s complement) plus 1 That is, add A to two’s complement of B D = A - B

Adder- Subtractor Circuit

Binary Subtraction Review from CSE 171 Two’s Complement Negative Numbers Binary Adder-Subtractors 4-bit Adder/Subtractor in VHDL

A 4-Bit Adder-Subtractor

addsub2 a(3:0) b(3:0) E CB SD(3:0) addsub2.vhd